Translation Residual Estimation As demonstrated in [1]}, residual estimation achieves better performance than direct regression by learning the distribution of the residual between the prior and actual value. The translation decoder \(\mathcal {F}_{t}\)  learns a 3D translation residual from the object translation prior \(t_{prior}\)  calculated as the average of predicted 3D coordinate over the sampled pixels in \(\mathcal {P}\) . To be more specific:
\(\begin{split}&t_{prior} = \frac{1}{N_p}\sum _{p\in N} K ^{-1} \left[u_p \ v_p \ 1\right]^T \hat{\mathcal {D}_p} \\&\hat{t} = t_{prior} + \mathcal {F}_{t}\left(\left[\mathcal {P}_{concat}, \mathcal {P}\right]\right) \\\end{split}\) 
